Isolating Segments, Fixed Point Index, and Symbolic Dynamics

Journal of Differential Equations

Volumn 161, Issue 2, 2000, Pages 245-288

  Wójcik, Klaudiusz ^a   Zgliczyński, Piotr ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Isolating segments; fixed point index; chaos; periodic solutions

Indexed keywords

EID: 0034148605     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3696     Document Type: Article

References (13)

1. Conley C. C. Isolated Invariant Sets and the Morse Index. CBMS. 38:1978;Amer. Math. Soc. Providence.
2. Dold A. Lectures on Algebraic Topology. 1972;Springer-Verlag, Berlin/Heidelberg/New York.
3. J. Guckenheimer, and, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York/Heidelberg/Berlin.
4. Galias Z., Zgliczyński P. Computer assisted proof of chaos in the Lorenz system. Physica D. 115:1998;165-188.
5. Srzednicki R. Periodic and bounded solutions in blocks for time-periodic nonautonomuous ordinary differential equations. Nonlinear Anal. 22:1994;707-737.
6. Srzednicki R. On detection of chaotic dynamics in ordinary differential equations. Nonlinear Anal. 30:1997;4927-4935.
7. Srzednicki R. On geometric detection of periodic solutions and chaos. Proceedings of the Conference Nonlinear Analysis and Boundary Value Problems, CISM Udine, October 2-6, 1995. CISM Courses and Lectures. 371:1996;Springer-Verlag, Wien/New York. p. 197-209.
8. Srzednicki R., Wójcik K. A geometric method for detecting chaotic dynamics. J. Differential Equations. 135:1997;66-82.
9. Wiggins S. Global Bifurcation and Chaos. Analytical Methods. 1998;Springer-Verlag, New York/Heidelberg/Berlin.
10. Wójcik K. Isolating segments and symbolic dynamics. Nonlinear Anal. 33:1998;575-591.
11. K. Wójcik, Chaos in nonautonomous periodic Hamiltonian systems on the plane, Internat. J. Bifur. Chaos, to appear.
12. Zgliczyński P. Fixed point index for iterations of maps, topological horseshoe and chaos. Nonlinear Anal. 8:1996;169-177.
13. Zgliczyński P. Computer assisted proof of chaos in the Hénon map and in the Rössler equations. Nonlinearity. 10:1997;243-252.